Question

Need some Help with this coordinate geometry problem. Will medal+ fan!!
Circle O has equation (x+2)^2 +(y-3)^2 =16. Circle K has equation (x-4)^2 + (y+1)^2=25. Relative to circle O and Circle K Where is point P(1,1)?
A. Inside circle C and Outside Circle K
B. Inside circle C and Circle K
C. Outside circle C and Inside Circle K
D. Outside circle C and Circle K
E. At one of the intersections of Circle O and Circle K?

Answer 1

Okay, here's where knowledge of the formulas will make your life much easier.

\[(x-h)^2 + (y-k)^2 = r^2\]is the general formula for a circle with radius \(r\) and center at \((h,k)\)

By comparing that with your formulas, you should be able to determine the radius and center of both circles. Make a sketch on a piece of paper and see where P(1,1) is in comparison to those two circles.

Answer 2

hint:
center of circle O is \(O=(-2,3)\), whereas center of circle K is \(K=(4,-1)\), now please compute the subsequent distances:
\(OP\), and \(KP\)

Answer 3

Distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) can be found with \[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]

Answer 4

OK, one sec..

Answer 5

radius is 4 for the first one

Answer 6

and 5 for the next one

Answer 7

that's right!

Answer 8

So what is the next step?

Answer 9

But you may not need to actually calculate any distances here, just make the diagram (carefully) and look at it.

Answer 10

How do you draw the circles?

Answer 11

Do you have a drawing compass? Failing that, a ruler?

Answer 12

I have a ruler

Answer 13

Here's a graph of the two circles for you:

Answer 14

It is B

Answer 15

Right? @whpalmer4

Answer 16

There's a website called https://www.geogebra.org that is useful for drawing these things, too. I don't use it myself, but many people here on OpenStudy do.

Yes, B appears to be correct, assuming I drew the right circles :-)

Answer 17

Ok, thanks!